Whakaoti i te 1/4+(2x-3x-1/8)=2/3(x+2/6)-2x

$$\frac{ 1 }{ 4 } +(2x- \frac{ 3x-1 }{ 8 } )= \frac{ 2 }{ 3 } ( \frac{ x+2 }{ 6 } )-2x$$

Whakaoti mō x

$$x=-\frac{1}{23}\approx -0.043478261$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 24, arā, te tauraro pātahi he tino iti rawa te kitea o 4,8,3,6.

$$6+48x-3\left(3x-1\right)=\frac{8}{3}\left(x+2\right)-48x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te 3x-1.

$$6+48x-9x+3=\frac{8}{3}\left(x+2\right)-48x$$

Pahekotia te 48x me -9x, ka 39x.

$$6+39x+3=\frac{8}{3}\left(x+2\right)-48x$$

Tāpirihia te 6 ki te 3, ka 9.

$$9+39x=\frac{8}{3}\left(x+2\right)-48x$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{8}{3} ki te x+2.

$$9+39x=\frac{8}{3}x+\frac{8}{3}\times 2-48x$$

Tuhia te \frac{8}{3}\times 2 hei hautanga kotahi.

$$9+39x=\frac{8}{3}x+\frac{8\times 2}{3}-48x$$

Whakareatia te 8 ki te 2, ka 16.

$$9+39x=\frac{8}{3}x+\frac{16}{3}-48x$$

Pahekotia te \frac{8}{3}x me -48x, ka -\frac{136}{3}x.

$$9+39x=-\frac{136}{3}x+\frac{16}{3}$$

Me tāpiri te \frac{136}{3}x ki ngā taha e rua.

$$9+39x+\frac{136}{3}x=\frac{16}{3}$$

Pahekotia te 39x me \frac{136}{3}x, ka \frac{253}{3}x.

$$9+\frac{253}{3}x=\frac{16}{3}$$

Tangohia te 9 mai i ngā taha e rua.

$$\frac{253}{3}x=\frac{16}{3}-9$$

Me tahuri te 9 ki te hautau \frac{27}{3}.

$$\frac{253}{3}x=\frac{16}{3}-\frac{27}{3}$$

Tā te mea he rite te tauraro o \frac{16}{3} me \frac{27}{3}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{253}{3}x=\frac{16-27}{3}$$

Tangohia te 27 i te 16, ka -11.

$$\frac{253}{3}x=-\frac{11}{3}$$

Me whakarea ngā taha e rua ki te \frac{3}{253}, te tau utu o \frac{253}{3}.

$$x=-\frac{11}{3}\times \frac{3}{253}$$

Me whakarea te -\frac{11}{3} ki te \frac{3}{253} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{-11\times 3}{3\times 253}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$x=\frac{-11}{253}$$

Whakahekea te hautanga \frac{-11}{253} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 11.

$$x=-\frac{1}{23}$$